1. Field of the Invention
This invention relates to a gravity balancer for a pivotal arm, and more particularly to a gravity balancing device for offsetting the gravitational moment of a rocking arm of a multi-articuate, teaching-playback type robot.
2. Description of the Prior Art
When operating a multi-articulated robot by electric or hydraulic motors, the major portion of the driving forces of these motors is consumed for offsetting the gravitational moments of the respective pivotal or rocking arms of the robot. Of course, such gravitational moment is desired to be reduced to a minimum, and in this regard it has been the conventional practice to resort to a balancing mechanism using a tension spring, a model arrangement of which is shown in FIG. 1.
In FIG. 1, indicated at 1 is an arm which is rockable about a a fixed pivotal point B, and at 2 a tension spring which is tensioned between a fixed point C located upwardly at a small distance a from the pivotal point B in vertical alignment therewith. Now, in a case where the distance between the two points A and B is R, the current length of the tension spring 2 is l, the load acting on the point A of the arm 1 is W, the tensile force of the spring 2 at the point A is F, the angle of the arm 1 with the horizontal line is .theta., and the angle of the tension spring 2 with the horizontal line is .alpha., the gravitational turn-over moment M.sub.1 of the pivoting arm 1 about point B is expressed by the following equation. EQU M.sub.1 =WR cos .theta. (1)
On the other hand, the moment M.sub.2 which is caused by the tension spring 2 is expressed by the equation EQU M.sub.2 =Fa cos .alpha. (2)
In this instance, if the free length of the tension spring 2 is L and the spring constant is k, the tensile force F is expressed by the following equation: EQU F=k.multidot.(l-L) (3)
Plotted on the graph of FIG. 2 are the curves of M.sub.1 and M.sub.2, by applying practical values of W=50 (kgf), R=1000 (mm), k=1 (kgf/mm) and a=200 (mm). In this graph the horizontal axis represents the angle of inclination .theta. of the arm, the vertical axis represents the moment (kgf.multidot.m) about point B, and the solid and broken lines indicate the gravitational moment M.sub.1 and the moment M.sub.2 caused by the tension spring 2, respectively. In this case, the free length L of the spring 2 is so determined as to balance the arm at .theta.=0.degree. and 90.degree..
In the graph of FIG. 2, the hatched area indicates the umbalancing gravitational force which amounts to 16 kgf.multidot.m maximum. As is clear therefrom, the conventional arrangement using a tension spring 2 can approximately balance the arm but is unable to maintain a completely balanced state. Namely, in FIG. 1, firstly with regard to the lengths of the arm and spring, such have a relationship as expressed by the following equation: EQU l cos .alpha.=R cos .theta. (4)
Therefore, M.sub.1 =M.sub.2 is the condition of the perfect balance, and, from equation (1) and (2), EQU WR cos .theta.=Fa.multidot.(R/l) cos .theta. EQU R cos .theta.(W-a.multidot.(F/l)=0 (5)
In equation (5), R and cos .theta. do not necessarily take a value of 0, and the condition of perfect balance is EQU W-a.multidot.(F/l)=0 (6)
in which W and a are constants, so that EQU F/l=W/a: constant
Namely, it is necessary to satisfy the condition of F.infin.l. In other words, perfect balance cannot be achieved unless a tensile force F proportional to the length l is applied. However, the tension spring 2 has no tensile force in the closed length so that it is impossible to satisfy F=0 when l=0. This is the reason why the conventional mechanism is unable to perfectly balance the rocking arm.
A system which perfectly balances with the gravitational moment of a pivotal arm is required in the so-called direct teaching phase in which an operational movement is taugth by gripping the fore end of the robot arm in a power-off state. Needless to say, although it is desired that a robot arm can be moved lightly irrespective of the direction of movement when a multi-articulate arm is manually operated, the robot arm itself generally has a relatively large weight which is easy to lower by difficult to lift up. As a matter of fact, it hinders smooth manual teaching operation, and requires unnecessary torques of the servo control, coupled with the problem of low positioning accuracy in the playback phase.